- 
              mf_newforms •   Show schema
  Hide schema
   
        {'Nk2': 72704, 'analytic_conductor': 145.1360907138792, 'atkin_lehner_eigenvals': [[2, -1], [71, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': False, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [18176, 1, [1279, 15621, 3841], [2, 2, 2]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': -1, 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660943104, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': -1, 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'label': '18176.2.a.b', 'level': 18176, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 71], 'level_radical': 142, 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-3q^{3}-3q^{7}+6q^{9}-6q^{11}+5q^{13}+\\cdots', 'related_objects': ['EllipticCurve/Q/18176/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '18176.2.a', 'trace_display': [0, -3, 0, -3], 'traces': [1, 0, -3, 0, 0, 0, -3, 0, 6, 0, -6, 0, 5, 0, 0, 0, -4, 0, -1, 0, 9, 0, -3, 0, -5, 0, -9, 0, -6, 0, 7, 0, 18, 0, 0, 0, 8, 0, -15, 0, -6, 0, -5, 0, 0, 0, 7, 0, 2, 0, 12, 0, -6, 0, 0, 0, 3, 0, -10, 0, 2, 0, -18, 0, 0, 0, -16, 0, 9, 0, -1, 0, -1, 0, 15, 0, 18, 0, 12, 0, 9, 0, -12, 0, 0, 0, 18, 0, 5, 0, -15, 0, -21, 0, 0, 0, 4, 0, -36, 0], 'weight': 2, 'weight_parity': 1}
- 
              label 18176.2.a.b does not appear in mf_hecke_nf
          
- 
              mf_newspaces •   Show schema
  Hide schema
   
        {'ALdims': [134, 148, 146, 132], 'ALdims_eis_new': [0, 0, 0, 0], 'ALdims_eis_old': [11, 12, 12, 12], 'ALdims_old': [416, 443, 431, 431], 'Nk2': 72704, 'analytic_conductor': 145.1360907138792, 'char_conductor': 1, 'char_degree': 1, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [18176, 1, [1279, 15621, 3841], [1, 1, 1]], 'conrey_index': 1, 'cusp_dim': 2281, 'dim': 560, 'eis_dim': 47, 'eis_new_dim': 0, 'hecke_orbit_code': 33572608, 'hecke_orbit_dims': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 4, 11, 11, 11, 11, 14, 14, 14, 14, 18, 18, 18, 18, 22, 22, 24, 24, 24, 24, 34, 34, 36, 36, 38, 38], 'label': '18176.2.a', 'level': 18176, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 71], 'level_radical': 142, 'mf_dim': 2328, 'mf_new_dim': 560, 'num_forms': 48, 'plus_dim': 266, 'prim_orbit_index': 1, 'relative_dim': 560, 'sturm_bound': 4608, 'trace_display': [0, 0, 0, 0], 'traces': [560, 0, 0, 0, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 624, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 624, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 400, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 320, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 624, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 400, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 352, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, -416, 0, 0, 0, 0, 0, 0, 0, 320, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 1072, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0], 'weight': 2, 'weight_parity': 1}
- 
              source_label 18176.2.a.b does not appear in mf_twists_nf
          
- 
              hecke_orbit_code 4503599660943104 does not appear in mf_hecke_charpolys
          
- 
              label 18176.2.a.b does not appear in mf_newform_portraits
          
- 
              mf_hecke_traces •   Show schema
  Hide schema
   
        
                      - 
              id: 119848142
              {'hecke_orbit_code': 4503599660943104, 'n': 1, 'trace_an': 1}
- 
              id: 119848143
              {'hecke_orbit_code': 4503599660943104, 'n': 2, 'trace_an': 0}
- 
              id: 119848144
              {'hecke_orbit_code': 4503599660943104, 'n': 3, 'trace_an': -3}
- 
              id: 119848145
              {'hecke_orbit_code': 4503599660943104, 'n': 4, 'trace_an': 0}
- 
              id: 119848146
              {'hecke_orbit_code': 4503599660943104, 'n': 5, 'trace_an': 0}
- 
              id: 119848147
              {'hecke_orbit_code': 4503599660943104, 'n': 6, 'trace_an': 0}
- 
              id: 119848148
              {'hecke_orbit_code': 4503599660943104, 'n': 7, 'trace_an': -3}
- 
              id: 119848149
              {'hecke_orbit_code': 4503599660943104, 'n': 8, 'trace_an': 0}
- 
              id: 119848150
              {'hecke_orbit_code': 4503599660943104, 'n': 9, 'trace_an': 6}
- 
              id: 119848151
              {'hecke_orbit_code': 4503599660943104, 'n': 10, 'trace_an': 0}
- 
              id: 119848152
              {'hecke_orbit_code': 4503599660943104, 'n': 11, 'trace_an': -6}
- 
              id: 119848153
              {'hecke_orbit_code': 4503599660943104, 'n': 12, 'trace_an': 0}
- 
              id: 119848154
              {'hecke_orbit_code': 4503599660943104, 'n': 13, 'trace_an': 5}
- 
              id: 119848155
              {'hecke_orbit_code': 4503599660943104, 'n': 14, 'trace_an': 0}
- 
              id: 119848156
              {'hecke_orbit_code': 4503599660943104, 'n': 15, 'trace_an': 0}
- 
              id: 119848157
              {'hecke_orbit_code': 4503599660943104, 'n': 16, 'trace_an': 0}
- 
              id: 119848158
              {'hecke_orbit_code': 4503599660943104, 'n': 17, 'trace_an': -4}
- 
              id: 119848159
              {'hecke_orbit_code': 4503599660943104, 'n': 18, 'trace_an': 0}
- 
              id: 119848160
              {'hecke_orbit_code': 4503599660943104, 'n': 19, 'trace_an': -1}
- 
              id: 119848161
              {'hecke_orbit_code': 4503599660943104, 'n': 20, 'trace_an': 0}
- 
              id: 119848162
              {'hecke_orbit_code': 4503599660943104, 'n': 21, 'trace_an': 9}
- 
              id: 119848163
              {'hecke_orbit_code': 4503599660943104, 'n': 22, 'trace_an': 0}
- 
              id: 119848164
              {'hecke_orbit_code': 4503599660943104, 'n': 23, 'trace_an': -3}
- 
              id: 119848165
              {'hecke_orbit_code': 4503599660943104, 'n': 24, 'trace_an': 0}
- 
              id: 119848166
              {'hecke_orbit_code': 4503599660943104, 'n': 25, 'trace_an': -5}
- 
              id: 119848167
              {'hecke_orbit_code': 4503599660943104, 'n': 26, 'trace_an': 0}
- 
              id: 119848168
              {'hecke_orbit_code': 4503599660943104, 'n': 27, 'trace_an': -9}
- 
              id: 119848169
              {'hecke_orbit_code': 4503599660943104, 'n': 28, 'trace_an': 0}
- 
              id: 119848170
              {'hecke_orbit_code': 4503599660943104, 'n': 29, 'trace_an': -6}
- 
              id: 119848171
              {'hecke_orbit_code': 4503599660943104, 'n': 30, 'trace_an': 0}
- 
              id: 119848172
              {'hecke_orbit_code': 4503599660943104, 'n': 31, 'trace_an': 7}
- 
              id: 119848173
              {'hecke_orbit_code': 4503599660943104, 'n': 32, 'trace_an': 0}
- 
              id: 119848174
              {'hecke_orbit_code': 4503599660943104, 'n': 33, 'trace_an': 18}
- 
              id: 119848175
              {'hecke_orbit_code': 4503599660943104, 'n': 34, 'trace_an': 0}
- 
              id: 119848176
              {'hecke_orbit_code': 4503599660943104, 'n': 35, 'trace_an': 0}
- 
              id: 119848177
              {'hecke_orbit_code': 4503599660943104, 'n': 36, 'trace_an': 0}
- 
              id: 119848178
              {'hecke_orbit_code': 4503599660943104, 'n': 37, 'trace_an': 8}
- 
              id: 119848179
              {'hecke_orbit_code': 4503599660943104, 'n': 38, 'trace_an': 0}
- 
              id: 119848180
              {'hecke_orbit_code': 4503599660943104, 'n': 39, 'trace_an': -15}
- 
              id: 119848181
              {'hecke_orbit_code': 4503599660943104, 'n': 40, 'trace_an': 0}
- 
              id: 119848182
              {'hecke_orbit_code': 4503599660943104, 'n': 41, 'trace_an': -6}
- 
              id: 119848183
              {'hecke_orbit_code': 4503599660943104, 'n': 42, 'trace_an': 0}
- 
              id: 119848184
              {'hecke_orbit_code': 4503599660943104, 'n': 43, 'trace_an': -5}
- 
              id: 119848185
              {'hecke_orbit_code': 4503599660943104, 'n': 44, 'trace_an': 0}
- 
              id: 119848186
              {'hecke_orbit_code': 4503599660943104, 'n': 45, 'trace_an': 0}
- 
              id: 119848187
              {'hecke_orbit_code': 4503599660943104, 'n': 46, 'trace_an': 0}
- 
              id: 119848188
              {'hecke_orbit_code': 4503599660943104, 'n': 47, 'trace_an': 7}
- 
              id: 119848189
              {'hecke_orbit_code': 4503599660943104, 'n': 48, 'trace_an': 0}
- 
              id: 119848190
              {'hecke_orbit_code': 4503599660943104, 'n': 49, 'trace_an': 2}
- 
              id: 119848191
              {'hecke_orbit_code': 4503599660943104, 'n': 50, 'trace_an': 0}
- 
              id: 119848192
              {'hecke_orbit_code': 4503599660943104, 'n': 51, 'trace_an': 12}
- 
              id: 119848193
              {'hecke_orbit_code': 4503599660943104, 'n': 52, 'trace_an': 0}
- 
              id: 119848194
              {'hecke_orbit_code': 4503599660943104, 'n': 53, 'trace_an': -6}
- 
              id: 119848195
              {'hecke_orbit_code': 4503599660943104, 'n': 54, 'trace_an': 0}
- 
              id: 119848196
              {'hecke_orbit_code': 4503599660943104, 'n': 55, 'trace_an': 0}
- 
              id: 119848197
              {'hecke_orbit_code': 4503599660943104, 'n': 56, 'trace_an': 0}
- 
              id: 119848198
              {'hecke_orbit_code': 4503599660943104, 'n': 57, 'trace_an': 3}
- 
              id: 119848199
              {'hecke_orbit_code': 4503599660943104, 'n': 58, 'trace_an': 0}
- 
              id: 119848200
              {'hecke_orbit_code': 4503599660943104, 'n': 59, 'trace_an': -10}
- 
              id: 119848201
              {'hecke_orbit_code': 4503599660943104, 'n': 60, 'trace_an': 0}
- 
              id: 119848202
              {'hecke_orbit_code': 4503599660943104, 'n': 61, 'trace_an': 2}
- 
              id: 119848203
              {'hecke_orbit_code': 4503599660943104, 'n': 62, 'trace_an': 0}
- 
              id: 119848204
              {'hecke_orbit_code': 4503599660943104, 'n': 63, 'trace_an': -18}
- 
              id: 119848205
              {'hecke_orbit_code': 4503599660943104, 'n': 64, 'trace_an': 0}
- 
              id: 119848206
              {'hecke_orbit_code': 4503599660943104, 'n': 65, 'trace_an': 0}
- 
              id: 119848207
              {'hecke_orbit_code': 4503599660943104, 'n': 66, 'trace_an': 0}
- 
              id: 119848208
              {'hecke_orbit_code': 4503599660943104, 'n': 67, 'trace_an': -16}
- 
              id: 119848209
              {'hecke_orbit_code': 4503599660943104, 'n': 68, 'trace_an': 0}
- 
              id: 119848210
              {'hecke_orbit_code': 4503599660943104, 'n': 69, 'trace_an': 9}
- 
              id: 119848211
              {'hecke_orbit_code': 4503599660943104, 'n': 70, 'trace_an': 0}
- 
              id: 119848212
              {'hecke_orbit_code': 4503599660943104, 'n': 71, 'trace_an': -1}
- 
              id: 119848213
              {'hecke_orbit_code': 4503599660943104, 'n': 72, 'trace_an': 0}
- 
              id: 119848214
              {'hecke_orbit_code': 4503599660943104, 'n': 73, 'trace_an': -1}
- 
              id: 119848215
              {'hecke_orbit_code': 4503599660943104, 'n': 74, 'trace_an': 0}
- 
              id: 119848216
              {'hecke_orbit_code': 4503599660943104, 'n': 75, 'trace_an': 15}
- 
              id: 119848217
              {'hecke_orbit_code': 4503599660943104, 'n': 76, 'trace_an': 0}
- 
              id: 119848218
              {'hecke_orbit_code': 4503599660943104, 'n': 77, 'trace_an': 18}
- 
              id: 119848219
              {'hecke_orbit_code': 4503599660943104, 'n': 78, 'trace_an': 0}
- 
              id: 119848220
              {'hecke_orbit_code': 4503599660943104, 'n': 79, 'trace_an': 12}
- 
              id: 119848221
              {'hecke_orbit_code': 4503599660943104, 'n': 80, 'trace_an': 0}
- 
              id: 119848222
              {'hecke_orbit_code': 4503599660943104, 'n': 81, 'trace_an': 9}
- 
              id: 119848223
              {'hecke_orbit_code': 4503599660943104, 'n': 82, 'trace_an': 0}
- 
              id: 119848224
              {'hecke_orbit_code': 4503599660943104, 'n': 83, 'trace_an': -12}
- 
              id: 119848225
              {'hecke_orbit_code': 4503599660943104, 'n': 84, 'trace_an': 0}
- 
              id: 119848226
              {'hecke_orbit_code': 4503599660943104, 'n': 85, 'trace_an': 0}
- 
              id: 119848227
              {'hecke_orbit_code': 4503599660943104, 'n': 86, 'trace_an': 0}
- 
              id: 119848228
              {'hecke_orbit_code': 4503599660943104, 'n': 87, 'trace_an': 18}
- 
              id: 119848229
              {'hecke_orbit_code': 4503599660943104, 'n': 88, 'trace_an': 0}
- 
              id: 119848230
              {'hecke_orbit_code': 4503599660943104, 'n': 89, 'trace_an': 5}
- 
              id: 119848231
              {'hecke_orbit_code': 4503599660943104, 'n': 90, 'trace_an': 0}
- 
              id: 119848232
              {'hecke_orbit_code': 4503599660943104, 'n': 91, 'trace_an': -15}
- 
              id: 119848233
              {'hecke_orbit_code': 4503599660943104, 'n': 92, 'trace_an': 0}
- 
              id: 119848234
              {'hecke_orbit_code': 4503599660943104, 'n': 93, 'trace_an': -21}
- 
              id: 119848235
              {'hecke_orbit_code': 4503599660943104, 'n': 94, 'trace_an': 0}
- 
              id: 119848236
              {'hecke_orbit_code': 4503599660943104, 'n': 95, 'trace_an': 0}
- 
              id: 119848237
              {'hecke_orbit_code': 4503599660943104, 'n': 96, 'trace_an': 0}
- 
              id: 119848238
              {'hecke_orbit_code': 4503599660943104, 'n': 97, 'trace_an': 4}
- 
              id: 119848239
              {'hecke_orbit_code': 4503599660943104, 'n': 98, 'trace_an': 0}
- 
              id: 119848240
              {'hecke_orbit_code': 4503599660943104, 'n': 99, 'trace_an': -36}
- 
              id: 119848241
              {'hecke_orbit_code': 4503599660943104, 'n': 100, 'trace_an': 0}